Random restarts can relate to the RAM too.
I suggest you download this:
and if you have a burnable CD drive, and a spare CD-R, using something like Nero, write the ISO to a disc (Making sure it writes as an ISO, not as a data disc), and restart the computer with the disc in, making sure in BIOS (Del at boot up usually), its set to run from your DVD/CD drive first, and then whatever else, so it boots automatically.
Then let it run scans on your RAM. If it sees errors, shut down, pull out all but one RAM stick, and power on the computer again. If that receives no errors, put another in (if you have more than one), and take the other out, and so on, until you find the one causing it.
If you don't get any errors however, then at least you know its not that.